Battery operated wireless communication devices commonly use two separate reference clocks to fulfil separate functions in the system that must meet very different requirements.
A low frequency clock, typically 32.768 kHz, serves as time keeper, in particular during sleep or idle modes. This is often referred to as real-time clock (RTC). The implementation of the RTC focuses on minimizing power consumption. A typical RTC design consumes around a microwatt of power. Phase noise, especially at high frequency, is of no concern.
A second higher frequency clock, for example 26 MHz, 38.4 MHz or 48 MHz, is often used as a reference signal for one or more phase-locked loops from which receiver and transmitter carrier signals can be derived. With complex modulation schemes, the key performance parameter is phase noise. The drive strength of the crystal is important for phase noise because phase noise is the ratio of undesired power (in the surrounding frequency spectrum) to desired power at the oscillation frequency. Phase noise can be minimized by keeping circuit noise low and to use moderate to large signal swings (high and low levels) so that any circuit added noise represents a small perturbation in relative terms.
When the reference signal is scaled up to a carrier frequency the phase noise increases with the square of the frequency scaling factor. This mechanism makes it virtually impossible to use a low frequency like 32.768 kHz (typical RTC frequency) as a reference for RF signals.
The physical properties of low and high frequency crystal resonators are also very different which explains why different circuit architectures are typically used to drive them. Most RTC crystals are constructed based on a tuning-fork shaped resonator. Higher frequencies are generated using AT cut crystals vibrating in thickness sheer mode as would be understood.
FIG. 1 illustrates the electrical differences between typical RTC crystals and typical higher frequency crystals for RF when represented as a linear lumped model.
In this model, the so-called motional inductance is labelled 11, the motional capacitance 12, the equivalent series resistance 13, the shunt capacitance 14 and external (to the crystal package 17) load capacitors 15 (C1) and 16 (C2). The table below shows parameters for commonly available quartz crystals
Typical Typical ref ParameterRTCclock for RFNominal freq32.768 kHz38.4 MHz(11) Motional inductance, LM 6.7 kH 5.7 mH(12) Motional capacitance, CM 3.5 fF 3.0 fF(14) Shunt capacitance, CP 2.0 pF 1.5 pFTotal load capacitance, CTOT10 pF10 pF(13) Serial resistance, RS50 kΩ60 Ω
The lumped model parameters relate to various properties of an oscillator built around a particular crystal resonator. For example, for small series resistance values the oscillation frequency, fOSC, is given by the following expression (where Sqrt=square root):2π·fOSC=ωOSC=Sqrt [1/LM·(1/CM+1/CL)],where CL=CP+C1C2/(C1+C2) is the total load capacitance seen by the crystal resonator.
The motional capacitance, CM, is much smaller than the load capacitance. Therefore, the oscillation frequency is close to the self-resonant point between motional inductance and motional capacitance given by what is called the series resonant frequency:fS=1/(2π)/Sqrt [LM·CM].
Large load capacitances C1 and C2 increase the oscillation frequency slightly;
smaller load capacitances shift the frequency further away from fS. This mechanism is commonly used in digitally controlled crystal oscillators (DCXO) to fine-tune the crystal to the desired frequency. The nominal oscillation frequency fOSC is obtained when the crystal is loaded with the appropriate total load capacitance CL specified by the manufacturer. When a very small load is applied the frequency of oscillation will be higher and close to the series resonant frequency as would be understood.
The series resistance dampens any oscillations between the inductor and the capacitors. To maintain constant amplitude, a feedback current must be added into the crystal. This is normally achieved using a gain stage sensing the voltage at one port (21A, 21B) of the crystal and injecting current into the second crystal port (21B, 21A) in anti-phase with the sensed voltage. This voltage-to-current or transconductance stage 20 (Gm) may be implemented as the well-known Pierce crystal oscillator as illustrated in FIG. 2. Another common arrangement is the Colpitts oscillator.
The load (tuning) capacitors 15, 16 can be tuned to change the oscillation frequency fOSC of crystal 21 as explained above.
In steady-state conditions the transconductance stage 20 adds just enough current into the loop to balance out losses in the crystal device, that is to say that the power dissipated in the crystal is replenished by the transconductance stage 20. This is known as the Barkhausen condition for oscillation. The required gain can be approximated by the expression belowGm=4ωOSC2·RS·CL2  (1)
The power dissipation within the crystal is given by the power provided by the Gm current source, P=½ Gm VP2, where VP is the amplitude of the voltage signal across the crystal ports (21A, 21B). This must equal the power dissipated across the series resistor, P=½ RS IR2, therefore,IR=VP·Sqrt(Gm/RS).
The current generated by the Gm stage has an amplitude given by IG=Gm·VP. This current is smaller, typically much smaller, than the current amplitude through the resistor IG/IR=Sqrt(Gm·Rs)=ωOSC·RS·CL<1.
In other words, most of the current flows between the crystal and the load capacitors. The amplitude of the current passing through the load capacitor is given by IC=ωOSC·CL·VP. It is 90° out of phase with the current generated by the Gm stage, IG2+IC2=IR2.
The total amount of energy stored contained in the oscillation can be expressed in terms of the magnetic energy stored on the motional inductance, E=½ LM IR2. Alternatively, energy may be expressed in terms of the electric field energy held by the motional capacitor E=½CM VM2, where VM=(CL/CM) VP. The load capacitors store only a tiny fraction of the overall energy contained in the system when CM»CL.
Without feedback, oscillations decay exponentially with a time constant given by τ=2Q/ωOSC. The quality factor Q=ωOSC LM/RS is typically very large, in the order of tens or hundreds of thousands. This means the circuit reacts very slowly to any changes in external drive level.
When comparing low frequency and high frequency crystal resonators, one finds that the Gm needed to maintain oscillations (see Eqn (1)) of a high frequency crystal is several orders of magnitude larger than the one to sustain low frequency oscillation. With the figures in the above table, the 32.768 kHz crystal can resonate with a Gm of 1 μS (siemens) whereas the 38.4 MHz quartz must be driven with 1,000 μS. If the same amplitudes are used, the power dissipation of the two crystals differs by a factor of more than a thousand. Typical RTC oscillators consume less than 1 μW whereas high frequency DCXOs consume just over 1 mW.
For RTC oscillators the standard design approach is to use a digital invertor gate. Compared to the high frequency design this has much reduced Gm and noise requirements but also consumes much less current.
There exist several challenges to overcome when attempting to use a single high frequency crystal resonator in a dual mode driver circuit.
(A) How can the drive level (voltage and current amplitude) be lowered whilst keeping Gm almost unchanged? Compared to established high frequency designs power consumption must reduce by a factor of around 1,000 but at the same time Gm must be 1,000 times larger than that used in standard RTC buffer designs.
(B) How can most of the load capacitance be switched in or out without disturbing the oscillation? In particular, when the load capacitance is lowered, for example from 10 pF to 2 pF, the instantaneous voltage across the crystal can increase by a factor of 5, enough to potentially damage the Gm stage device.
Accordingly there is a need to design a circuit and method to overcome these challenges.